Moodle is developed in Linux using Apache, MySQL, and PHP (also known as the LAMP platform). If you have a choice, this is the preferred environment to be used.
Go to http://download.moodle.org to download Moodle. As you can see, there are quite a number of distributions to choose from:
For the current version of Moodle, there are two releases: the latest stable build and the latest official release. The latest stable version is created weekly (every Wednesday) and is the best choice for a new server. The latest official release contains the stable build as well as new fixes, but the version will not have gone through the weekly code review and might contain unresolved issues.
Versions that are older than the current one are maintained by the Moodle development team, and bug fixes are back-ported. Sometimes newly added functionality is back-ported. Currently, the oldest supported version is 1.6, but this will certainly change in the future...